An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <-3 N , 1 N># and the second is #F_2 = < 6 N, -2 N>#. What is the object's rate and direction of acceleration?

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Answer 1 · 2018-07-04T08:56:37

#a=F/m#

HINT: The acceleration #a# of a rigid body of mass #m# under the application of force #F# is given as follows

#a=F/m#

Answer 2 · 2018-07-04T09:45:12

The rate of acceleration is #=1.58ms^-2# in the direction #18.43^@# clockwise from the x-axis

The resultant of the #2# forces is

#vecF=vecF_1+vecF_2#

#=<-3,1> +<6,-2>#

#= <3, -1>#

#vecF=mveca#

The mass is #m=2kg#

Therefore,

The acceleration is

#veca=vecF/m=1/2 *<3,-1> = <3/2,-1/2>#

The rate of acceleration is

#||veca|| = ||<3/2,-1/2>|| = sqrt((3/2)^2+(-1/2)^2)#

#=sqrt(9/4+1/4)#

#=sqrt10/2#

#=1.58ms^-2#

The direction of acceleration is

#theta=arctan(-1/3)=18.43^@# clockwise from the x-axis